Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
//                I know stuff but probably my rating tells otherwise...

//               Kya hua, code samajhne ki koshish kar rhe ho?? Mat karo,
//                      mujhe bhi samajh nhi aata kya likha hai


import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class _1294F {
    static LinkedList<Integer> adj[];
    static int node1,node2,node3, level;
    static int vis[];
    static TreeSet<Integer> path = new TreeSet<>();
    static void Mangni_ke_bail_ke_dant_na_dekhal_jye() {
        n = ni();
        adj = new LinkedList[n + 1];
        vis = new int[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new LinkedList<>();
        for (int i = 1; i < n; i++) {
            int x = ni(), y = ni();
            adj[x].add(y);
            adj[y].add(x);
        }

        node1 = 1;
        level = 0;
        dfs(node1, level, 0);
        level = 0;
        vis = new int[n + 1];
        dfs(node1, level, 1);
        vis = new int[n + 1];
        path.add(node2);
        dfspath(node1);
        //pl(path);
        vis = new int[n + 1];
        //for(int i:path)vis[i]=1;
        level = 0;
        for (int i : path) {
            for (int j : adj[i])
                dfs1(j, 1);
        }
        pl(path.size() - 1 + level);
        if (node3 != 0)
            pl(node1 + " " + node2 + " " + node3);
        else {
            path.remove(node1);
            path.remove(node2);
            pl(node1 + " " + node2 + " " + path.first());
        }
    }

    static void dfs(int i, int lev, int y) {
        if (vis[i] == 1) return;
        vis[i] = 1;
        if (level < lev) {
            level = lev;
            if (y == 0)
                node1 = i;
            else node2 = i;
        }
        for (int x : adj[i]) dfs(x, lev + 1, y);
    }

    static boolean dfspath(int i) {
        if (i == node2) return true;
        boolean temp = false;
        if (vis[i] == 1) return false;
        vis[i] = 1;
        for (int x : adj[i]) temp |= dfspath(x);
        if (temp) path.add(i);
        return temp;
    }

    static void dfs1(int i, int lev) {
        if (vis[i] == 1) return;
        vis[i] = 1;
        if (path.contains(i)) return;
        if (lev > level) {
            node3 = i;
            level = lev;
        }
        for (int x : adj[i]) dfs1(x, lev + 1);
    }

    //----------------------------------------The main code ends here------------------------------------------------------
    /*-------------------------------------------------------------------------------------------------------------------*/
    //-----------------------------------------Rest's all dust-------------------------------------------------------------


    static int mod9 = 1_000_000_007;
    static int n, m, l, k, t;
    //static AwesomeInput input = new AwesomeInput(System.in);
    static AwesomeInput input;
    static BufferedWriter bw;

    static PrintWriter pw ;

    static long power(long a, long b) {
        if (b == 0) return 1;
        if ((b & 1) == 1) return a * power(a * a, b >> 1);
        return power(a * a, b >> 1);
    }

    // The Awesome Input Code is a fast IO method //
    static class AwesomeInput {
        private InputStream letsDoIT;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        private AwesomeInput(InputStream incoming) {
            this.letsDoIT = incoming;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = letsDoIT.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        private long ForLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        private String ForString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);
        }
    }

    // functions to take input//
    static int ni() {
        return (int) input.ForLong();
    }

    static String ns() {
        return input.ForString();
    }

    static long nl() {
        return input.ForLong();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o) {
        pw.print(o + "");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    // Fast Sort is Radix Sort
    public static int[] fastSort(int[] f) {
        int n = f.length;
        int[] to = new int[n];
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    public static void main(String[] args) {      //threading has been used to increase the stack size.
        try{
            input = new AwesomeInput(System.in);
            pw = new PrintWriter(System.out, true);
//            input = new AwesomeInput(new FileInputStream("/home/saurabh/Desktop/input.txt"));
//            pw = new PrintWriter(new BufferedWriter(new FileWriter("/home/saurabh/Desktop/output.txt")), true);

        }
        catch(Exception e){}

        new Thread(null, null, "AApan_gand_hawai_dusar_ke_kare_dawai", 1 << 25)  //the last parameter is stack size desired.
        {
            public void run() {
                try {
                    double s = System.currentTimeMillis();
                    Mangni_ke_bail_ke_dant_na_dekhal_jye();
                    //System.out.println(("\nExecution Time : " + ((double) System.currentTimeMillis() - s) / 1000) + " s");
                    pw.flush();
                    pw.close();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
}